Plasma is the fourth state of matter. 99% of the matter in the universe is in plasma state. The presence of charged particles in plasma and their ability to create and interact with electromagnetic fields, gives rise to many phenomena which are not present in ordinary fluids and solids. The main source of energy for the mankind, the Sun, is a plasma phenomenon. The most important application of plasma is to generate power in thermonuclear fusion reactor. Various types of wave occur within the plasma. Collisions between plasma particles reduce the amplitude of the wave and the energy is transferred from the wave field to the plasma particles. If the energy is transferred from plasma particle to the wave field, then amplitude of the wave increases. This gives instabilities. Instabilities complicate the confinement of plasma in the laboratory. Instabilities are necessary to study for controlled thermonuclear fusion research. In this paper parametric instability, oscillating two stream instability and parametric decay instability are discussed. Also, the third moment equation and its derivation are discussed in detail. This book may be helpful to the students studying instabilities.